What is the integral from 8 to 12 of 2/(x^3) ?

The integral from 8 to 12 of 2/(x^3) is 5/576

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integral from 8 to 12 of 2/(x^3)

\int_{8}^{12} \frac{2}{x ^{3}} d x

\frac{5}{576}

Decimal

0.00868 \dots

Solution steps

\int_{8}^{12} \frac{2}{x ^{3}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{8}^{12} \frac{1}{x ^{3}} d x

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{8}^{12}

= 2 [- \frac{1}{2 x ^{2}}]_{8}^{12}

Compute the boundaries:

\frac{5}{1152}

= 2 \cdot \frac{5}{1152}

Simplify

= \frac{5}{576}

\int (x ln (x))^{2} d x

\frac{\partial}{\partial x} (y e^{y})

\frac{\partial}{\partial x} (5 x y^{3} + 15 x y - 4 y^{2})

\frac{d}{d x} (x^{2} \cdot y^{3})

x \to 0 lim (x sin (\frac{7 π}{x}))

What is the integral from 8 to 12 of 2/(x^3) ?
The integral from 8 to 12 of 2/(x^3) is 5/576